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Quizzes > Quizzes for Business > Education

Test Your Skills: Multi-Step Equations Practice Quiz

Sharpen Your Equation Solving Techniques Today

Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art depicting a multi-step equations practice quiz.

Inspired by Joanna Weib's clear and encouraging style, this Multi-Step Equations Practice Quiz offers a dynamic collection of algebra problems to boost equation solving skills and confidence. Students and educators can engage with real-world scenarios while receiving instant feedback on each answer. The quiz is fully editable - modify any question in the built-in editor to fit classroom needs or personal study goals. For deeper practice, try the Linear Equations Assessment Quiz or tackle the Algebra: Linear Equations and Graphs Quiz, or explore more quizzes for comprehensive review.

Solve for x: 2x + 5 = 11.
x = 3
x = 6
x = -3
x = 2
Subtracting 5 from both sides gives 2x = 6, and dividing by 2 yields x = 3. This isolates x correctly by reverse operations.
Solve for x: 3x - 4 = 11.
x = 7/3
x = -5
x = 3
x = 5
Adding 4 to both sides gives 3x = 15, and dividing by 3 yields x = 5. Each step reverses the subtraction and multiplication.
Solve for x: x/4 + 2 = 5.
x = 8
x = 12
x = 24
x = 3
Subtracting 2 from both sides gives x/4 = 3. Multiplying both sides by 4 yields x = 12. This applies additive and multiplicative inverses.
Solve for x: 7 = 2x + 3.
x = -2
x = 2
x = 1/2
x = 3
Subtracting 3 from both sides gives 2x = 4, and dividing by 2 yields x = 2. The operations maintain balance at each step.
Solve for x: -3x + 9 = 0.
x = 9
x = -3
x = 3
x = 0
Subtracting 9 from both sides gives -3x = -9. Dividing by -3 yields x = 3. Inverse operations successfully isolate x.
Solve for x: 2(x + 3) = 14.
x = -4
x = 7
x = 4
x = 2
Distribute to get 2x + 6 = 14, then subtract 6 to get 2x = 8 and divide by 2 to find x = 4. Distribution and inverse operations isolate the variable.
Solve for x: 4x - 5 = 3x + 7.
x = 12
x = 2
x = -2
x = 1
Subtract 3x from both sides to get x - 5 = 7, then add 5 to both sides to find x = 12. Combining like terms isolates x.
Solve for x: (x/3) - 2 = 4.
x = 24
x = 18
x = 12
x = 6
Add 2 to both sides giving x/3 = 6, then multiply by 3 to get x = 18. Each step reverses the prior operation.
Solve for x: 5(x - 2) + 3 = 2x + 7.
x = 11/3
x = 3
x = 14/3
x = 4
Expand to 5x - 10 + 3 = 2x + 7, simplify to 5x - 7 = 2x + 7, subtract 2x to get 3x = 14, then divide by 3 to find x = 14/3.
Solve for x: 3(2x + 1) - 4 = 5x + 2.
x = -1
x = 4
x = 2
x = 3
Distribute to get 6x + 3 - 4 = 5x + 2, simplify to 6x - 1 = 5x + 2, subtract 5x then add 1 to get x = 3.
Solve for x: -2(3x - 4) = 5x + 6.
x = 2/11
x = -2/11
x = -2
x = 10
Distribute to get -6x + 8 = 5x + 6, add 6x and subtract 6 to get 8 - 6 = 11x, so 2 = 11x and x = 2/11.
Solve for x: (x - 2)/5 + 1 = (2x + 3)/10.
No solution
x = 5
x = 1
x = -7
Multiply by 10: 2(x - 2) + 10 = 2x + 3, simplify to 2x + 6 = 2x + 3, which reduces to 6 = 3, a contradiction, so no solution exists.
Solve for x: (3x + 2)/4 = x - 1.
x = 6
x = -6
x = 4
x = 2
Multiply both sides by 4: 3x + 2 = 4x - 4, then subtract 3x and add 4 to get x = 6. Inverse operations isolate x.
Solve for x: 2x + (x/2) = 10.
x = 6
x = 5
x = 4
x = 3
Combine like terms by multiplying both sides by 2: 4x + x = 20, so 5x = 20 and x = 4. This balances and simplifies the expression.
Solve for x: 4 - 2(x + 2) = x.
x = -4
x = 2
x = 1
x = 0
Distribute to get 4 - 2x - 4 = x, which simplifies to -2x = x, so x = 0. Each operation maintains the equation's balance.
Twice the sum of a number and 3 equals five more than three times the number. What is the number?
x = -1
x = 3
x = 1
x = 2
Set up 2(x + 3) = 3x + 5, expand to 2x + 6 = 3x + 5, then subtract 2x and 5 to get x = 1.
The sum of three consecutive even integers is 42. Find the integers.
12, 14, 16
13, 15, 17
10, 12, 14
14, 16, 18
Let the integers be x, x+2, x+4. Their sum 3x + 6 = 42 gives x = 12, so the integers are 12, 14, and 16.
Solve for x: 3(x - 1) + 2(x + 4) = 5x + 6.
No solution
x = 2
x = -2
x = 1
Expand to 3x - 3 + 2x + 8 = 5x + 6, simplify to 5x + 5 = 5x + 6, which reduces to 5 = 6, a contradiction, so there is no solution.
Solve for x: (2x + 3)/3 + (x - 1)/4 = 3.
x = 3
x = 11/27
x = 27/11
x = 5/3
Multiply both sides by 12 to get 4(2x + 3) + 3(x - 1) = 36, simplify to 11x + 9 = 36, then solve 11x = 27 to find x = 27/11.
A service has a fixed fee plus a per-item cost. If 5 items cost $23 and 8 items cost $32, find the fixed fee and the per-item cost.
Fixed fee $7; per-item cost $2
Fixed fee $8; per-item cost $3
Fixed fee $10; per-item cost $2.5
Fixed fee $5; per-item cost $4
Let F + 5p = 23 and F + 8p = 32. Subtracting gives 3p = 9 so p = 3, then substitute to find F = 23 - 15 = 8.
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Learning Outcomes

  1. Analyse multi-step equations to isolate variables effectively
  2. Apply inverse operations accurately across multiple steps
  3. Identify common pitfalls and strategies in equation solving
  4. Demonstrate proficiency in balancing and simplifying expressions
  5. Master real-world word problems involving multi-step equations
  6. Evaluate solutions to ensure correctness and completeness

Cheat Sheet

  1. Understand the Order of Operations (PEMDAS) - Think of PEMDAS as your roadmap for solving equations correctly! Always tackle Parentheses first, then Exponents, Multiplication and Division (left to right), and finish with Addition and Subtraction (left to right). Following this sequence will save you from silly mistakes and math mayhem! Solving Multi-Step Equations Guide
  2. Apply the Distributive Property - The distributive property is like spreading peanut butter evenly on bread: multiply each term inside the parentheses by the outside factor to simplify your equation. This step clears out clutter and turns complex-looking problems into straightforward ones. Practice makes perfect, so distribute away! Distributive Property Lesson
  3. Combine Like Terms - Grouping like terms is your secret weapon for decluttering equations - add or subtract variables and constants that match to shrink your problem size. It's like organizing a messy room by putting similar items together! Once like terms are combined, you'll have a much cleaner path to the solution. Combining Like Terms Tutorial
  4. Isolate the Variable - To find the value of x, y, or any other variable, use inverse operations (think opposite moves) on both sides until the variable stands alone. Just like undoing a knot, you reverse each step to free the variable! Keep everything balanced by doing the same operation to both sides. Multi-Step Equations Explained
  5. Handle Fractions and Decimals - Fractions and decimals can make equations feel like a tricky maze, but multiplying both sides by the least common denominator or 10/100/etc. clears them out in one go! This approach transforms pesky fractions into whole numbers, making calculations smoother and faster. Say goodbye to messy decimals! Clearing Fractions with LCD
  6. Check Your Solutions - Don't rush off - always plug your answer back into the original equation to see if it really works. This simple check catches arithmetic blunders and ensures your solution is rock-solid. Think of it as proof-reading your math work before hitting "submit"! Solution Verification Tips
  7. Avoid Common Mistakes - Watch out for sneaky errors like forgetting to distribute to every term, combining unlike terms, or dropping minus signs! Spot these traps by working step-by-step and double-checking each move. A little caution goes a long way toward error-free equations. Sidestepping Common Mistakes
  8. Practice Word Problems - Turn real-life scenarios into equations by defining variables, setting up relationships, and solving step-by-step. It's like translating a story into the language of math - super rewarding once you crack the code! The more word problems you tackle, the sharper your problem-solving skills become. Word Problems Practice
  9. Use a General Strategy - Adopt a consistent approach: simplify each side, eliminate fractions/decimals, isolate the variable term, then solve. This checklist keeps you organized, so you never miss a step in multi-step equations. Over time, this strategy becomes second nature! General Strategy Guide
  10. Stay Positive and Persistent - Treat each equation like a puzzle waiting to be solved and view mistakes as clues, not setbacks. Celebrate small wins, take short breaks, and keep that math spirit high - you'll be mastering multi-step equations in no time! More Motivation & Tips
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